Question

Examine the sequence 13,10,7,4,.....is an AP

Answer 1

Check the differences of consecutive terms:

13 - 10 = 3
10 - 7 = 3
7 - 4 = 3

The difference is constant. Hence it is an AP

Answer 2

Yes the sequence 13 , 10 , 7 , 4 , . . . . is an AP

Given :

The sequence 13 , 10 , 7 , 4 , . . . .

To find :

Examine the sequence 13 , 10 , 7 , 4 , . . . . is an AP

Concept :

A sequence of numbers are said to form an Arithmetic progression if the difference between any two consecutive terms is always the same.

Solution :

Step 1 of 2 :

Write down the given sequence

Here the given sequence is 13 , 10 , 7 , 4 , . . . .

Step 2 of 2 :

Determine sequence 13 , 10 , 7 , 4 , . . . . is an AP or not

First term = a₁ = 13

Second term = a₂ = 10

Third term = a₃ = 7

.

.

Now

a₂ - a₁ = 10 - 13 = - 3

a₃ - a₂ = 7 - 10 = - 3

So on

Thus we get , a₂ - a₁ = a₃ - a₂

Since the difference between any two consecutive terms is same , which is - 3

So the given sequence is an arithmetic progression.

Hence the sequence 13 , 10 , 7 , 4 , . . . . is an AP

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